9 research outputs found
Supervised Functional PCA with Covariate Dependent Mean and Covariance Structure
Incorporating covariate information into functional data analysis methods can
substantially improve modeling and prediction performance. However, many
functional data analysis methods do not make use of covariate or supervision
information, and those that do often have high computational cost or assume
that only the scores are related to covariates, an assumption that is usually
violated in practice. In this article, we propose a functional data analysis
framework that relates both the mean and covariance function to covariate
information. To facilitate modeling and ensure the covariance function is
positive semi-definite, we represent it using splines and design a map from
Euclidean space to the symmetric positive semi-definite matrix manifold. Our
model is combined with a roughness penalty to encourage smoothness of the
estimated functions in both the temporal and covariate domains. We also develop
an efficient method for fast evaluation of the objective and gradient
functions. Cross-validation is used to choose the tuning parameters. We
demonstrate the advantages of our approach through a simulation study and an
astronomical data analysis.Comment: 24 pages, 15 figure